Writing Algebraic Expressions

Show your work for each problem.

1.
Which expression represents "the sum of a number and 8"?
1. a)
2. b)
3. c)
4. d)
Answer:
"Sum" means addition. The sum of a number and 8 is written as .
2.
Which expression represents "triple a number"?
1. a)
2. b)
3. c)
4. d)
Answer:
"Triple" means three times or multiply by 3. Triple a number is or simply .
3.
Write an expression for "a number increased by 5". Use for the number.
Answer: n + 5
"Increased by 5" means adding 5 to the number. So increased by 5 is .
4.
Write an expression for "a number divided by 4". Use for the number.
Answer: x/4
"Divided by 4" means , which we write as or x/4.
5.
Which expression represents "7 less than a number"?
1. a)
2. b)
3. c)
4. d)
Answer:
"7 less than a number" means start with the number and subtract 7. So it's , NOT .
6.
Which expression represents "twice a number plus 3"?
1. a)
2. b)
3. c)
4. d)
Answer:
"Twice a number" = , then "plus 3" = . Together: . Note: would be "twice the SUM of a number and 3".
7.
Write an expression for "5 more than twice a number". Use for the number.
Answer: 2x + 5
"Twice a number" = . "5 more than" means add 5: .
8.
Write an expression for "the product of 4 and a number, decreased by 6". Use for the number.
Answer: 4n - 6
"Product of 4 and a number" = . "Decreased by 6" = . Answer: .
9.
A movie ticket costs 15 dollars. Write an expression for the total cost of tickets plus a 10 dollar snack.
Answer: 15t + 10
1. What is the cost of one ticket? 15
2. How do you write the cost of tickets? 15t
3. What is the cost of the snack? 10
4. What is the total cost expression? 15t + 10
10.
Write an expression for "a number decreased by 4, then multiplied by 3". Use for the number.
Answer: 3(n - 4)
1. What does "decreased by 4" mean? subtract 4
2. How do you write "a number decreased by 4"? n - 4
3. Now this result gets multiplied by 3. Do you need parentheses? yes
4. What is the final expression? 3(n - 4)
11.
Which expression represents "twice the sum of a number and 5"?
1. a)
2. b)
3. c)
4. d)
Answer:
"The sum of a number and 5" = . "Twice" that sum means multiply by 2: . Note: means "twice a number, plus 5" - different!
12.
Write an expression for "the quotient of a number and 3, increased by the number itself". Use for the number.
Answer: n/3 + n
"Quotient of a number and 3" = . "Increased by the number itself" = . Answer: .
13.
A taxi charges 3 dollars to start plus 2 dollars per kilometer. Write an expression for the cost of a kilometer ride.
Answer: 3 + 2k
1. What is the starting cost? 3
2. What is the cost per kilometer? 2
3. How do you write the cost for kilometers? 2k
4. What is the total cost expression? 3 + 2k
14.
Write an expression for "half of a number, minus 3, then doubled". Use for the number.
Answer: 2(x/2 - 3)
1. How do you write "half of a number"? x/2
2. Now subtract 3 from that. What do you have? x/2 - 3
3. This result gets doubled. Do you need parentheses? yes
4. What is the final expression? 2(x/2 - 3)
15.
A phone plan costs 25 dollars per month plus 5 cents per text. Write an expression for the monthly cost with texts.
Answer: 25 + 0.05t
1. What is the fixed monthly cost in dollars? 25
2. What is the cost per text in dollars? 0.05
3. How do you write the cost for texts? 0.05t
4. What is the total monthly cost expression? 25 + 0.05t
16.
Which phrase matches the expression ?
1. a)9 decreased by a number
2. b)A number decreased by 9
3. c)A number divided by 9
4. d)9 times a number
Answer: A number decreased by 9
means start with and subtract 9. That's "a number decreased by 9." Note: "9 decreased by a number" would be .